- Education and Science
Mayan Mathematics and Numbers - Symbols of Their Culture
Mayan Math Is Not That Hard
My fascination with the ancient Mayan culture has finally led me to a math lesson. While I readily admit that math wasn’t my favorite subject in school, I definitely can appreciate the Mayan approach to math. They were quite advanced for their time.
This hub explores the more simple aspect of Mayan math: how they wrote their numbers and how their numbers related to their concept of time.
© C. Calhoun 2012. All rights reserved.
Where the Mayans Lived - Present Day Central America, Including the Yucatan Peninsula
The Concept of Zero
By the end of the third century, the Mayans had already figured how to use the number zero. They used a shell to represent it. They figured that though it didn’t presently have “matter,” it could actually have matter at some future point in time.
Interestingly, the Mayans had the number zero figured out ahead of many other civilizations.
Books and References
The Mayan Numeral System Was Directly Tied to Their Calendar and to the Concept of Time
The Mayan calendar told them when to plant crops, marked the changing seasons, and even when to celebrate their religious rites.
Because of the Mayans’ ability to use the number zero and write just about any number they could imagine, they could use their calendar to predict events thousands of years into the future.
The calendar was made of two wheels. They meshed together to make a 365-day year.
The year looked different than our present method of keeping track of days, months and years. Their calendar was 18 months long, with each month containing 20 days each. The Mayans considered the 5 days at the end of the year to be bad luck.
The Mayan notion of a day was that each day had a certain amount of “contents.” At the end of the day, when empty, another day would arrive, ready with its own contents.
The Mayan concept of time wasn’t linear, either. To them, it was cyclical. Because of their use of the wheel, they expected events to repeat themselves in the future.
For a particular day to repeat itself, though, 52 years had to pass. The Calendar Wheel was a cycle of 52 years. It is noteworthy, though, that for the Mayans, time neither had a beginning nor an end.
The Mayan Math System Used a Base 20 Approach
Remember how the Mayan calendar had 20 days in each month? That’s a reflection of their way of doing numbers.
In the United States and in many other industrialized societies, the decimal system is the mathematical approach of these cultures. The root deci means “ten.” It is a system that uses base 10.
The Mayans, however, used a base 20 form of mathematics.
Their mathematical symbols comprised of three characters: a shell, dots and bars.
The shell = 0.
The dot = 1.
The bar = 5.
Thus, the numbers 1-19 were made of the shell, dots and numbers. (See photo.)
The number 36 could be written as a power of 20: 1 x 20 = 20 and 20 + 16 = 36. If you compare that to the decimal system, it looks different: 3 x 10 = 30 and 30 + 6 = 36.
Here’s where it gets a little more complicated. Since the Mayan system was base 20, things changed after number 19: they moved to the next place value.
Another interesting point is that the Mayans wrote their place values vertically. The smallest number went on the bottom, and progressively higher numbers went on top, based on powers of 20. (see table)
The 1s place was at the bottom, then the 20s (20 x 1) place above that, then the 400s place (20 x 20), followed by the 8000s (20 x 20 x 20), then the 160,000 (20 x 20 x 20 x 20), and so on.
Thus, if you wanted to write the number 35 (see examples in red below), you would use all 19 numbers in the ones place, and a "twenty" in the 20s place.
Mayan Numbers 85, 37 and 92 Written Out
The Number 18,425 in Mayan Numbers
Power of 20
20 x 20 x 20 x 20
20 x 20 x 20
2 eight thousands
20 x 20
6 four hundreds
20 x 1
1 x 0